a triangle has an area of 20 inches squared. every dimension of the triangle is multiplied by a scale factor, and the new triangle has an area of 180 inches squared. what was the scale factor?
area scaled by 9
dimensions scaled by √9 = 3
To find the scale factor, we need to compare the areas of the two triangles. The scale factor is the square root of the ratio of their areas.
Let's denote the scale factor as "x".
The given area of the first triangle is 20 inches squared. If we multiply all dimensions of the triangle by the scale factor "x", we get the second triangle with an area of 180 inches squared.
Now, we can set up an equation using the ratio of the areas:
(20 * x^2) / 20 = 180 / 20
Simplifying this equation gives us:
x^2 = 180 / 20
x^2 = 9
To solve for "x", we take the square root of both sides:
x = √9
x = 3
Therefore, the scale factor is 3.